If `a,b,c epsilon N` the number of points having vector `aveci+bvecj+cveck` such that `6lea+b+cle10` is (A) 90 (B) 110 (C) 105 (D) 200

If a,b,cepsilon N then number of points having positions vector aveci+bvecj+cveck such that 5 lea+b+cle10 is (A) 120 (B) 116 (C) 100 (D) none of these

If a,b,c epsilon {1,2,3,4,5}, the number of equations of the form ax^2+bx+c=0 which have real roots is (A) 25 (B) 26 (C) 27 (D) 24

Let a,b,c in N, then number of ordered triplet (a,b,c) such that 5a+6b+3c=50

A,B,C and D have position vectors a,b,c and d, respectively, such that a-b=2(d-c). Then,

The number of points having position vector a hat i + b hat j + c hatk , where 1 leq a,b,cleq10 and a,b,c in N, such that 2^a + 3^b+5^c is a multiple of 4 is (A) 1000 (B) 500 (C) 250 (D) 125

Two vectors have magnitudes 6 and 8 units, respectively. Find the magnitude of the resultant vector if the angle between vectors is (a) 60^(@) (b) 90^(@) and ( c ) 120^(@) .

56, 72, 90, 110, 132, 150 (a) 72 (b) 110 (c) 132 (d) 150

If a, b, c and d are four coplanr points, then prove that [a b c]=[b c d]+[a b d]+[c a d] .

The number of pilgrims in the group is (a) 4 (b) 6 (c) 8 (d) 10